here probability=P(X+Y<1)= f(x,y) dy dx =e-(x+y) dy dx =-e-x*e-y |1-x0 dx
=e-x(1-e-1+x) dx=(e-x-e-1) dx =(-e-x-xe-1)|10 =0.2642
Let X and Y be random losses with joint density function and 0 otherwise. An insurance...
An insurance policy covers losses X and Y which have joint density function 24y f(x,y) , y>0. (a) Find the expected value of X (b) Find the probability of a payout if the policy pays X + 2Y subject to a deductible of 1 on X and 1 on 2Y. (c) Find the probability of a payout if the policy pays X +2Y subject to a deductible of 2 on the total payment X + 2Y An insurance policy covers...
3. Let the random variables X and Y have the joint probability density function 0 y 1, 0 x < y fxy(x, y)y otherwise (a) Compute the joint expectation E(XY) (b) Compute the marginal expectations E(X) and E (Y) (c) Compute the covariance Cov(X, Y)
Exercise 6.55 Let X and Y be random variables with joint density function f(x, y)- 4 0 otherwise Show that the joint density function of U = 3(X-Y) and V = Y is otherwise, where A is a region of the (u, v) plane to be determined. Deduce that U has the bilateral exponential distribution with density function fu (11) te-lul foru R. Exercise 6.55 Let X and Y be random variables with joint density function f(x, y)- 4 0...
24. Let X and Y be continuous random variables with joint density function 4xy for 0 < x, y 1 f(x, y) otherwise. What is the probability of the event X given that Y ?
Let X and Y be random variables with joint density function F(x,y) O<ysi< otherwise The marginal density of Y is fr() = 3 (1 - ), for 0 < y<1. True False
Let X and Y be random variables with joint density function f(x,y) бу 0 0 < y < x < 1 otherwise The marginal density of Y is fy(y) = 3y (1 – y), for 0 < y < 1. True False
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...
Let the random variable X and Y have the joint probability density function. fxy(x,y) lo, 3. Let the random variables X and Y have the joint probability density function fxy(x, y) = 0<y<1, 0<x<y otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X,Y).
3. Let the random variables X and Y have the joint probability density function fxr (x, y) = 0 <y<1, 0<xsy otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X,Y).
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V Y